On Weakly Primary Submodules

Let  R  be a commutative ring with non-zero identity.  A proper submodule  N of an  R-module  M  is weakly primary if     implies   or   for some positive integer n.  A number of results concerning weakly primary submodules are given.  For example,  we give other characterization of weakly primary submodules.   Also various properties of weakly primary submodules are considered.  For example we show that if  N  is a weakly primary submodule of an  R-module  M  which is not primary,  then IN = 0  for every ideal .